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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Countably Infinite Sets
Replies: 11   Last Post: Dec 28, 2012 9:08 PM

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forbisgaryg@gmail.com

Posts: 43
Registered: 11/26/12
Re: Countably Infinite Sets
Posted: Dec 28, 2012 9:08 PM
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On Friday, December 28, 2012 6:16:32 AM UTC-8, netzweltler wrote:
> On 28 Dez., 03:49, "Ross A. Finlayson" <ross.finlay...@gmail.com>
>
> wrote:
>
> > On Dec 27, 6:43 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> >
>
> > > Does the set {{1}, {1,2}, {1,2,3}, ...} contain all natural numbers?
>
> >
>
> > What does "..." mean?
>
>
>
> "..." means, there is a bijection to the natural numbers
>
>
>
> 1 -> {1}
>
> 2 -> {1,2}
>
> 3 -> {1,2,3}
>
> ...
>
>
>
> >
>
> > Many would include zero.
>
>
>
> I cannot see the difference. I could also have asked:
>
> Does the set {{0}, {0,1}, {0,1,2}, ...} contain all natural numbers?

You set contains sets that are subsets of all natural numbers.
You set contains no natural numbers, only sets.

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